conchoid

A shell-shaped curve. Given a point A and a curve C, if
we pick a point Q on C and draw a line L through
A and Q and mark points P and P' on
L at some fixed distance in either direction from Q, then
the locus of P and P' as Q moves on C
is a conchoid.

The conchoid of Nicomedes is a conchoid in which the given
line is a straight line; i.e., given a line C and a point A
we pick a point Q on C, draw a line L through
A and Q, and mark P and P' on L
at some fixed distance from Q. The conchoid of Nicomedes is the
locus of P and P' as Q moves along C.
It has the polar equation r = a sec θ + k.

The conchoid of de Sluze is the curve with the Cartesian
equation a(x - a)(x2 + y2)
= k2x2.